Algebra, pls help
1 answer:
Answer:
Product of 6 and a number would be 6.
Nine more than a number?
Combine a number and 7? Either 7x or x + 7.
Step-by-step explanation:
Question 1 is relatively simple. 6 is a constant, so it can be inserted into any equation and maintain the same value. "A number" could represent anything, so we'll represent it with a variable. This gives you 6x (also 6*x)
Question 2 is the same as the first with 1 more step added to it. A number, as previously stated, is represented by the variable x. You divide this by the constant value of 2 to give you . Nine more would add +9 to the expression. Your final answer would be
.
Question 3. Combine is a bit vague, but it could be either addition or multiplication. This could give you either or
.
Hope it was helpful.
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Answer:
-2, 8/3
Step-by-step explanation:
You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...
A = (1/2)(f(a) +f(4))(4 -a)
= (1/2)((3a -1) +(3·4 -1))(4 -a)
= (1/2)(3a +10)(4 -a)
We want this area to be 12, so we can substitute that value for A and solve for "a".
12 = (1/2)(3a +10)(4 -a)
24 = (3a +10)(4 -a) = -3a² +2a +40
3a² -2a -16 = 0 . . . . . . subtract the right side
(3a -8)(a +2) = 0 . . . . . factor
Values of "a" that make these factors zero are ...
a = 8/3, a = -2
The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.
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<em>Alternate solution</em>
The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.
5 = 5 (g + h)
1 = g + h
1 - h = g
g = 1 - h
Answer: g = 1 - h.
1 = g + h
1 - h = g
g = 1 - h
Answer: g = 1 - h.